Changing the k constant in voltage potential equation?

[falconblade]

Summary:: What if you were calculating the voltage potential for a dipole, but underwater?

I'm making a predictive model (in R programming) for the voltage potential at any point around a dipole. I need to be able to change parameters, one being the k constant.

V=( kpcosѲ)/(r^2).
Where V is voltage, k is the constant (N m^2/C^2), p is the dipole moment (p=qd), and r is pretty much the distance.
(attaching a page from textbook over this)

I need the k constant changed because I am simulating this underwater, with conductivity (μS/cm) taking the place of my k constant. Any ideas on how to approach this? Far fetched but, is there a way to convert μS to N m^2/C^2?

 

[Dr_Nate]

The constant you are trying to change is $$k=\frac{1}{4\pi\epsilon_0}.$$ Where $\epsilon_0$ is the vacuum permittivity. To use the dipole equation in a material you need to multiply $\epsilon_0$ by the relative permittivity of the material $\epsilon_r$.

For water at 20 degrees Celsius, $\epsilon_r\approx 80$. Be aware, though, that it is very temperature dependent. It also sounds like you have impurities causing conductivity, so that's likely going to change the value too.

 

[rude man]

Summary:: What if you were calculating the voltage potential for a dipole, but underwater?

Summary:: What if you were calculating the voltage potential for a dipole, but underwater?

I'm making a predictive model (in R programming) for the voltage potential at any point around a dipole. I need to be able to change parameters, one being the k constant.

V=( kpcosѲ)/(r^2).
Where V is voltage, k is the constant (N m^2/C^2), p is the dipole moment (p=qd), and r is pretty much the distance.
(attaching a page from textbook over this)

I need the k constant changed because I am simulating this underwater, with conductivity (μS/cm) taking the place of my k constant. Any ideas on how to approach this? Far fetched but, is there a way to convert μS to N m^2/C^2?

Is it fresh or salt water?
If salt you aso need to consider conductivity which is very large in salt water whch consists mostly of ionized sodium and chlorine.
If fresh conductivity might be low enough to ignore, depends again on the salinity of the water.